科研之友
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摘要
Denote by w(A) the numerical radius of a bounded linear operator A acting on Hilbert space. Suppose that A is invertible and that w(A) %26lt;= 1+epsilon and w(A(-1)) %26lt;= 1+epsilon for some epsilon %26gt;= 0. It is shown that inf{parallel to A-U parallel to : U unitary} %26lt;= c epsilon(1/4) for some constant c %26gt; 0. This generalizes a result due to J.G. Stampfii, which is obtained for epsilon = 0. An example is given showing that the exponent 1/4 is optimal. The more general case of the operator rho-radius w(rho)(.) is discussed for 1 %26lt;= rho %26lt;= 2.
- 出版日期2013-6
